But you forget all the other things that then need to be moved 15 minutes forward:
School buses
School taxis (Yes they do get used in many rural areas)
Crossing patrols
Parking restrctions outside schools
Caretakers hours
Teaching assistants hours
and probably many more.
It isn't that simple!
Also needing to change would be:
Catering staff hours
Deliveries - at least at my old school these were always timed to avoid breaks and lunchtime
Any before and/or after school clubs, and the hours of the staff who run them (who may or may not be employed by the school)
Possibly the timing of sports matches with other schools
Probably the working hours of some parents who time their day around school hours
Local service bus provision - if routes are infrequent then services around school starting and finishing times are often strengthened or run a different route to better serve the school.
Times when the school facilities by the local community - swimming pools and gyms for example are often used by adults before work. This will mean leisure centre staff's hours will likely need to change.
And there are still likely things that have not been mentioned.
At least most of these things are not impossible to change, but it will require significant effort and time - in some cases on the order of months - and any changes would need to be aligned with the start of a school term (September, January or March/April depending when Easter falls). So it really is far from "simple" as suggested.